Most currently used approximations for the one-particle Green's function G in the framework of many-body perturbation theory, such as Hedin's GW approximation or the cumulant GW+C approach, are based on a linear-response approximation for the screened interaction W. The extent to which such a hypothesis is valid and ways to go beyond have been explored only very little. Here we show how to derive a cumulant Green's function beyond linear response from the equation of motion of the Green's function in a functional derivative formulation. The results can be written in a compact form, which opens the possibility to calculate the corrections in a first-principles framework using time-dependent density functional theory. In order to illustrate the potential importance of the corrections, numerical results are presented for a model system with a core level and two valence orbitals.

We demonstrate theoretically that an array of carbon nanoscrolls acts as a hyperbolic magnetic metamaterial in the terahertz regime with genuine subwavelength operation corresponding to a wavelength-to-structure ratio of about 200. Due to the low sheet resistance of graphene, the electromagnetic losses in an array of carbon nanoscrolls are almost negligible, offering a very sharp magnetic resonance of extreme positive and negative values of the effective magnetic permeability. The latter property leads to superior imaging properties for arrays of carbon nanoscrolls which can operate as magnetic endoscopes in the terahertz range where magnetic materials are scarce. Our optical modeling is supplemented with ab initio density functional calculations of the self-winding of a single layer of graphene onto a carbon nanotube so as to form a carbon nanoscroll. The latter process is viewed as a means to realize ordered arrays of carbon nanoscrolls in the laboratory based on arrays of aligned carbon nanotubes which are now routinely fabricated.Metamaterials are artificial materials which exhibit response characteristics that are not observed in the individual responses of their constituent materials, characteristics such as artificial magnetism, negative refractive index, near-field amplification, cloaking, and optical illusions. 1 The basic functionalities of metamaterials stem from the occurrence of electric and magnetic resonances wherein the electromagnetic field (EM) field is strongly localized within subwavelength volumes. Their magnetic response is associated with the induction of strong currents in illuminated metamaterials. These strong currents, in turn, can lead to strong paramagnetic (permeability μ > 1) and diamagnetic behavior (permeability μ < 1 or even μ < 0) in the near-infrared and optical regions where such a response is not met in naturally occurring materials. Magnetic activity in these regions of the EM spectrum is of great technological importance, since it allows for the realization of devices such as compact cavities, adaptive selective lenses, tunable mirrors, isolators, converters, optical polarizers, filters, and phase shifters. 2 The basic requirement for defining a given artificial EM structure as a metamaterial is its subwavelength nature, i.e., the operating wavelength being much larger than the characteristic length, (e.g., period) of the structure. The higher the wavelength-to-structure ratio, the most efficient the operation of metamaterials is. Namely, undesirable effects related with the corresponding effective-medium parameters, i.e., the effective electric permittivity eff and magnetic permeability μ eff , are sufficiently mitigated. Such effects are, for example, the wave-vector dependence due to the spatial inhomogeneity 3 or the antiresonance behavior and the concomitant unnatural negative imaginary parts for eff and/or μ eff . 4 To the best of our knowledge, the deepest subwavelength metamaterial design reported so far has been the so-called "Swiss roll" array, 5 a two-dimensional...